How to Name Node Groups
You can name your node group after exiting node group edit view, by selecting the Node Group and editing the text in the name box directly, or on the Properties Tool Shelf > Properties Panel to the left, while the group is selected.

Your Node Groups will be automatically erased once they have no users in your file, that means it is not used in any material and they have no Fake Users (pressing the F button to the right of the name.

Have in mind that in Blender data isn't truly deleted until your restart Blender.
That means Materials, Node Groups, Mesh or Object data, and everything else.

If you press the delete button it will stick around during that session with a Zero number in front of the name stating that it as no users. It will only be truly deleted after you restart Blender